A spline-based nonhomogeneous poisson process for modelling crime patterns in Akwa Ibom State, Nigeria

A non-homogeneous Poisson process (NHPP) accounts for varying intensities, permitting more flexibility by accommodating a varying intensity function over time. Choosing an appropriate functional form for this intensity function remains a gap, which this study seeks to fill. Given the crime dynamics globally, this study employs an NHPP with a splinebased Poisson regression function to model crime occurrences in Akwa Ibom State between 2018 and 2023. A six-year crime dataset (consisting of 41 crime types) was obtained from the Akwa Ibom State Police Command. Having identified the most frequent crime- murder with 240 cases and 153 arrests, Anscombe’s variance stabilisation transformation method was applied in testing for the homogeneity of the data. Poisson regression model with spline was thereafter explored in estimating the intensity function of NHPP, with the data divided into quarters. As earlier hinted, this study focuses on the reported murder cases, which were observed to have a periodic pattern. The result shows that the use of the Poisson regression model with spline succeeded in overcoming the limitation of an NHPP and that the seasonal effect for each quarter was approximately 3. It is also estimated that the state would record an average of 7 murder cases between 15th November 2024to 21st December 2024. Thus, with this study, the prospect of crime forecasting is not only possible but can be improved upon; thereby contributing to the broader field of crime analysis. Besides, this study offers a new methodological approach to crime modelling that could be applied in other regions or types of crimes.